Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19097801 | C2 | semidirect |
| 2. C2×#19097796 | C2 | semidirect |
| 3. C2×#19097759 | C2 | semidirect |
| 4. #23757665 | C2 | semidirect |
| 5. #23757660 | C2 | semidirect |
| 6. #23757655 | C2 | semidirect |
| 7. C4×#14578938 | C2 | semidirect |
| 8. #532×C157 | C2 | semidirect |
| 13. C2×#14578944 | C22 | semidirect |
| 14. C2×#14578942 | C22 | semidirect |
| 22. #19097682 | C22 | semidirect |
| 23. C4×#11929434 | C22 | semidirect |
| 25. C4⋊Q8×C157 | C22 | semidirect |
| 26. #127×C157 | C22 | semidirect |
| 27. #124×C157 | C22 | semidirect |
| 43. #14578938 | D4 | semidirect |
| 106. C157 | #3153 | semidirect |
| 110. #532 | D157 | semidirect |
| 126. C4⋊Q8 | C2×D157 | semidirect |
| 127. #127 | C2×D157 | semidirect |
| 131. #124 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097801 | 2 |
| C2×#19097796 | 2 |
| C2×#19097759 | 2 |
| #23757665 | 2 |
| #23757660 | 2 |
| #23757655 | 2 |
| C4×#14578938 | 2 |
| #532×C157 | 2 |
| #3153 | 157 |